Now that we understand how to find the mean, let’s have a look at how to apply standard deviation.

Remember that we had a look at this equation earlier in the course:

(hat{sigma} = sqrt{frac{Sigma ((x – bar{x})^2)}{n-1}})

Up to now, we gained an understanding all of the pieces of information in this formula:

• (n) = the number of scores
• (x) = the data set we are working with
• (bar{x}) = average of the data set
• (Sigma) = the sum of the data set

We should now be able to put all of this knowledge together to calculate the Standard Deviation. Let’s have a look at this in small steps using our ages from the previous examples:

Starting with (x):
(x = 30, 21, 59, 45)

Now, let’s calculate (bar{x}):
(bar{x} = frac{30 + 21 + 59 + 45}{4})
(therefore bar{x} = 38.75)

Next, let’s look at how we can calculate (Sigma):
(Sigma ((x – bar{x})^2) = (30 – 38.75)^2 + (21 – 38.75)^2 + (59 – 38.75)^2 + (45 – 38.75)^2)
(therefore Sigma ((x – bar{x})^2) = (-8.75)^2 + (-17.75)^2 + (20.25)^2 + (6,25)^2)
(therefore Sigma ((x – bar{x})^2) = 76.5625 + 315.0625 + 410.0625 + 39.0625)
(therefore Sigma ((x – bar{x})^2) = 840.75)

And remember that we have four points of data, so:
(n = 4)

Let’s apply all of these into our formula:
(hat{sigma} = sqrt{frac{Sigma ((x – bar{x})^2)}{n-1}})
(therefore hat{sigma} = sqrt{frac{840.75}{4-1}})
(therefore hat{sigma} = sqrt{frac{840.75}{3}})
(therefore hat{sigma} = sqrt{280.25})
(therefore hat{sigma} = 16.74)

We shall discuss what standard deviation means later in this course. For now, we are learning how to apply formulas to statistics.

Join the discussion

How are you feeling about tackling complex formulas now that you understand the basics of formula structure and how to tackle them by breaking them into smaller parts before trying to solve them?

Use the discussion section below and let us know your thoughts. Try to respond to at least one other post and once you’re happy with your contribution, click the Mark as Complete button to check the Step off, then you can move to the next step.